Rechargeable batteries are the most commonly used energy source of modern port-able electronic appliances. Additionally rechargeable batteries are very often used as back-up energy sources in applications where uninterrupted supply of electrical power is needed. The basic area of application of the present invention is in solutions of the latter kind, although the general principles of battery modeling and model-based predicting can also be used for other purposes. The battery type that is especially discussed in this patent application is the VRLA (Valve Regulated Lead Acid) battery, but the invention is equally applicable to all kinds of rechargeable batteries for which comparable mathematical models can be presented.
It is typical to UPS (Uninterrupted Power Supply) applications that only relatively seldom comes a real need for using the power stored in the batteries. However, if and when such a situation occurs, it should be certain that the performance and energy supplying capacity of the batteries is good enough. Internal electrochemical processes of the batteries cause slow but inevitable decrease in performance, which should be somehow accounted for. A “brute force” solution is to replace all batteries with new ones according to a predefined timetable, but because the timetable must in that case include an ample safety margin, it is clear that also batteries that would still be perfectly usable will be replaced. A more elegant solution is to compose a mathematical model of the structure and behaviour of a battery, to perform some basic voltage, current and temperature measurements and to use these as inputs to the mathematical model to obtain a prediction of the behaviour of the battery in a discharge situation. Only if such a mathematically calculated prediction indicates that the performance level of a battery may not be sufficiently high any more, an alarm is generated to alert a human operator about the need of replacing the battery. Using mathematical models to describe the behaviour of actual physical processes that take place inside a battery is often referred to as soft-sensor characterization, because the modeling software produces similar “measurement” results as could be obtained by placing measuring devices inside the battery.
Mathematical simulation of lead-acid batteries has been treated in various prior art publications, including but not being limited to J. Newman and W. Tiedemann: “Simulation of Recombination Lead-Acid Batteries”, J. Electrochem. Soc. vol. 144, no. 9, pp. 3081-3091,1997; H. Gu, C. Y. Wang and B. Y. Liaw: “Numerical Modeling of Coupled Electrochemical and Transport Processes in Lead-Acid Cell”, J. Electrochem. Soc. vol. 144, no. 6, pp. 2053-2061, 1997; and J. Landfors, D. Simonsson and A. Sokirko: “Mathematical Modelling of a Lead-Acid Cell with Immobilized Electrolyte”, Journal of Power Sources, no. 55, pp. 217-230, 1995. These publications are incorporated herein by reference.
FIGS. 1a, 1b and 1c illustrate schematically certain conventional principles of simulating the behaviour of a battery or arrangement of batteries when they are used as a power source. FIG. 1a shows the situation to be simulated: a battery 101 is coupled to a load 102 in order to provide the load with an operational voltage V and an electric current I. A set of parameter values 103 is known that describe the structure and state of the battery 101. An explicitly shown parameter value is the temperature T of the battery, which is measured continuously or regularly with a measuring arrangement 104. Simulating aims at providing an answer to the question: starting from the moment when the battery 101 is coupled to the load 102 to replace a normally used power source, how long time will it take before the battery 101 is discharged so much that it can not sustain a sufficient supply of electric energy to the load 102?
The terms “back-up time” and “cut-off time” are used (sometimes even a bit confusingly) to define two slightly different kinds of answers. Back-up time is defined in relation to the remaining capacity of the battery 101, usually so that back-up time ends when 90 percent of the original battery capacity has been used up. Cut-off time is defined in relation to a sufficient voltage level. Cut-off occurs when the voltage per cell in the battery 101 drops below a certain minimum level, for which different values may exist depending on load current. A widely used cut-off voltage level for VRLA batteries under high-rate discharge is 1.55 volts per cell.
FIG. 1b illustrates a known trivial method which has relatively little to do with actual mathematical simulation. The method of FIG. 1b is based on the fact that one has obtained a large set of experimental data and composed a look-up table where each of a large number of potentially occurring initial conditions is associated with a corresponding experimentally verified back-up or cut-off time. At step 111 the present state of the battery is checked by obtaining up-to-date values for certain parameters. At step 112 these actual parameter values are compared with those that have been stored as indicators of starting conditions in the experimentally handled example cases, and those stored parameter values are selected that match the actual values as closely as possible. At step 113 there is simply read from the look-up table that experimentally obtained back-up or cut-off time that has been associated with the selected initial condition parameter values.
FIG. 1c illustrates a known more simulation-oriented approach. Again at step 121 certain parameter values are obtained that describe the present state of the battery. The simulation algorithm sets a TIME variable to zero at step 122 and calculates at step 123 the value of the voltage V that can be obtained with the parameter values as they are. At step 124 the simulation algorithm checks, whether the obtained volt-age value is above the above-mentioned minimum level. If the mathematical model handles battery capacity instead of voltage, steps 123 and 124 are adapted so that battery capacity replaces voltage. Typically at this stage the result of step 124 positive, because the simulation calculations are only at the very beginning. Therefore the algorithm proceeds to step 125 where it increases the value of the TIME variable by a certain relatively short simulation interval dt in order to simulate the passing of time. Thereafter the simulation algorithm calculates at step 126, how did the parameter values change during the simulation interval dt. A return to step 123 occurs so that the simulation algorithm now calculates a new value for the voltage V (or the battery capacity) that takes into account the new parameter values calculated at step 126. Again the newly calculated voltage value (or battery capacity) is checked against the minimum level at step 124. The algorithm executes the loop that consists of steps 125,126, 123 and 124 in this order over and over again until at some stage the calculated voltage value or battery capacity value fails the test in step 124. Thereafter the algorithm exits the loop into step 127 and announces the final value of the TIME variable as the length of time it took for the battery to discharge.
The drawback of prior art simulation methods and devices is mainly their limited accuracy in predicting the actual behaviour of a battery. The simulation approach shown in FIG. 1c is only as good as are the assumptions made about the time-dependent behaviour of the parameters that describe the state of the battery. Even a small inaccuracy in the predicted behaviour of a parameter may lead to remarkable deviations from a correct result, because the typically relatively large number of simulation steps that are taken before the voltage or capacity value drops below the minimum level has a tendency to amplify the effect of such inaccuracies.